Volume equations for poplars growing on farmland in Sweden

Abstract

Volume equations for poplars growing on farmland in Sweden. The aim of the study was to construct a simple volume equation for poplar and to evaluate the equation together with seven published equations. Data from 72 poplars were collected from 37 stands in central and southern Sweden (lat. 55–60°N). The stands’ mean age and density was 21 years and 940 stems ha^?1, respectively and the trees’ mean diameter at breast height (DBH) was 25 cm. One simple volume equation with three parameters to be estimated for poplar was constructed with DBH and total height (H) as independent variables. This equation was analyzed and compared to seven published simple equations. The best performance, in terms of low values of Root Mean Square Error (RMSE) and Absolute Bias, was achieved by the equations developed by Eriksson and by Scott. However, due to these equations high level of multicollinearity an alternative recommendation was made where the constructed equation is recommended.     

Comparison of model forms for estimating stem taper and volume in the primary conifer species of the North American Acadian Region

? The performance of ten commonly used taper equations for predicting both stem form and volume in balsam fir [Abies balsamea (L.) Mill], red spruce[Picea rubens (Sarg.)], and white pine[Pinus strobus (L.)] in the Acadian Region of North America was investigated.

? Results show that the Kozak (2004) and Bi (2000) equations were superior to the other equations in predicting diameter inside bark for red spruce and white pine, while the Valentine and Gregoire (2001) equation performed slightly better for balsam fir.

? For stem volume, the Clark et al. (1991) equation provided the best predictions across all species when upper stem diameter measurements were available, while the Kozak (2004) and compatible taper equation of Fang et al. (2000) performed well when those measurements were unavailable.

? The incorporation of crown variables substantially improved stem volume predictions (mean absolute bias reduction of 7–15%; root mean square error reduction of 10–15%) for all three species, but had little impact on stem form predictions.

? The best taper equation reduced the predicted root mean square error by 16, 39, and 45% compared to estimates from the widely used Honer (1965) regional stem volume equations for balsam fir, red spruce, and white pine, respectively.

? When multiple taper equations exist for a certain species, the use of the geometric mean of all predictions is an attractive alternative to selecting the “best” equation.

     

Biomass production of hybrid aspen growing on former farm land in Sweden

We construct dry weight equations for hybrid aspen growing on former farmland in Sweden. Dry weight equations for fractions of hybrid aspen trees were also made. We estimated biomass production in 24 stands. The stands were located in Sweden at latitudes ranging from 55 to 60o N. The mean age was 18 years (range 15-23), the mean stand density 1090 stems·ha-1 (range 378 2374), and the mean diameter at breast height (over bark) 178 mm (range 85 244 mm). Soil types in the hybrid aspen stands were mainly clay (21 stands), tills (2 stands) and other (1 stand). The mean total standing dry weight above stump level (≈ 200 mm) for the hybrid aspen stands was 135±53 t·ha-1 with a range of 42 219 t·ha-1 . In addition to estimating conventional dry weights of trees and tree components, basic density, specific leaf area (SLA), projected leaf area (PLA) and leaf area index (LAI) were estimated and were in agreement with published figures.     

墨西哥瓦瓦州州东北部橡树商品材材积核算系统

比较了Kozak（1988）,Bi（2000）和Fang等（2000）的削度模型,形成了橡树商品材材积核算系统。在所研究的不同树龄、不同密度的松树．橡树混交林内,采集了298株橡树削度数据。结果表明,Fang等（2000）建立的可兼容分段模型可以很好地描述实验数据,可用于估测树木在指定树高的直径、树高一指定直径比、商品材材积量和总体积。本研究建立的公式可作为该研究区内森林调查的基本工具,简便、易于操作。统计分析结果表明,尽管本研究所建立的公式具有局地适应性,但仍可应用于其他区域。图4表4参53。     

基于分位数回归的华北落叶松干形曲线模拟

干形是反映树干外部形态的重要指标,也是评价干材价值的重要依据,而削度方程是描述树木干形好坏的一个重要定量指标,其对干形模拟的准确性直接决定着树干材积和森林蓄积的估算结果。以河北省塞罕坝机械林场华北落叶松人工林为研究对象,基于4个常见的简单削度方程,模拟了260株样木的干形曲线,采用调整后决定系数(Ra^2)、均方根误差(RMSE)、平均误差(ME)和平均误差绝对值(MAE)评价模型的拟合效果和检验效果,筛选最优的基础模型,并利用分位数回归技术,构建人工华北落叶松干形曲线模型。结果表明,4个简单削度方程中,Kozak方程对华北落叶松干形的拟合效果最好(Ra^2=0.934,RMSE=1.985cm),检验结果也是最优的(ME=0.125cm,MAE=1.212cm)。因此,基于Kozak方程,结合分位数回归技术建立了华北落叶松干形曲线,相较于基础模型,分位数回归模型的拟合优度进一步提高。当分位点设置为0.1时,模型对靠近下部和上部的树干干形拟合效果较好;当分位点设置为0.5时,模型对位于中部的树干干形拟合效果较好;当分位点设置为0.9时,模型对树干基部的拟合效果较好。可见,分位数回归技术使模型具有更强的灵活性。     

Segmented taper equations with crown ratio and stand density for Dahurian Larch (<Emphasis Type="Italic">Larix gmelinii</Emphasis>) in Northeastern China

Segmented taper equation was selected to model stem profile of Dahurian larch (Larix gmelinii Rupr.). The data were based on stem analysis of 74 trees from Dailing Forest Bureau in Heilongjiang Province, Northeastern China. Two taper equations with crown ratio and stand basal area were derived from the Max and Burkhart’s (1976) taper equation. Three taper equations were evaluated: (1) the original equation, (2) the original equation with crown ratio, and (3) the original equation with basal area. SAS NLIN a...     

Stem Form and Taper Changes After Thinning and Nitrogen Fertilization in Picea abies and Pinus sylvestris Stands

Stem form and taper changes after thinning and thinning combined with N fertilization were studied in 23 Norway spruce [Picea abies (L.) Karst.] and 46 Scots pine (Pinus sylvestris L.) stands in Sweden observed for 5-28 yrs. Average taper was calculated for the stem section 1.3-6.0 m above ground level and as the ratio between the diameter at breast height and total tree height for periods of 5-10 yrs. At the start of the experiment, before the first thinning, the dominant height was 12-15 m. Once 65% of the basal area had been removed in a single thinning from below, the remaining trees showed a strong increase in taper compared with trees in unthinned stands. Stems in stands treated with heavily recurrent thinnings from below also increased in taper, although the increases were not always statistically significant. Trees in thinned, N-fertilized Scots pine stands in middle and northern Sweden developed a more pronounced taper compared with stems in equally thinned, unfertilized stands.     

Stem taper function for sweet chestnut (Castanea sativa Mill.) coppice stands in northwest Spain

? Context

Despite the economic importance of Castanea sativa Mill. in northwest Spain, studies of its growth and yield are practically non-existent.

? Aims

A compatible system formed by a taper function, a total volume equation, and a merchantable volume equation was developed for chestnut (C. sativa Mill.) coppice stands in northwest Spain.

? Methods

Data from 203 destructively sampled trees were used for the adjustment. Outliers were removed with a non-parametric local adjustment, providing a final data set of measurements taken from 3,188 sections which was used to test five taper models (compatible and non-compatible). A second-order continuous autoregressive error structure was used to model the error term and account for autocorrelation. Presence of multicollinearity was evaluated with the condition number. Comparison of the models was carried out using overall goodness-of-fit statistics and graphical analysis.

? Results

Results show that the models developed by Fang et al. in For Sci 46: 1–12, 2000 and Kozak in For Chron 80, N 4: 507–515, 2004 were superior to other equations in predicting diameter for chestnut coppice stands.

? Conclusion

The compatible volume system developed by Fang et al. in For Sci 46: 1–12, 2000 was finally selected as it provided the best compromise between describing stem profile and also estimating merchantable height, merchantable volume, and total volume and therefore provides the first specific tool for more effective management of chestnut coppice stands.     

Developing a taper model for the Pinus elliottii × P. caribaea var. hondurensis hybrid in South Africa

A relatively new hybrid, Pinus elliottii × P. caribaea var. hondurensis (Pexc), for which a taper model does not exist, is being planted commercially in South Africa. This study primarily focused on developing a taper model for Pexc in South Africa. Taper data were collected from a total of 363 trees, in the Mpumalanga and Limpopo provinces, using a random sampling method. A subsample was selected to determine if altitude, rainfall, temperature or soil have a significant influence on the taper of Pexc. Only rainfall significantly influenced the overall taper. The Max and Burkhart segmented polynomial taper model, as well as the Kozak88, Kozak01 and Kozak02 variable exponent taper models, were fitted, compared and tested using the statistical analysis system (SAS). The predictive ability of the models was evaluated based on the results from the mean bias, standard deviation, the standard error of prediction and the average percentage deviation. The Kozak02 model had the best fit overall followed by the Max and Burkhart model (MB76). The MB76 model, however, predicted the volumes more accurately than the Kozak02 model.     

Stem taper functions for maritime pine (<Emphasis Type="Italic">Pinus pinaster</Emphasis> Ait.) in Galicia (Northwestern Spain)

A total of 31 taper functions from 3 different groups of models (single, segmented and variable-form taper functions) were fitted to diameter-height data from 203 Pinus pinaster trees sampled across even-aged stands in Galicia (northwestern Spain). Most of the taper functions analyzed showed problems of multicollinearity as indicated by the condition number. A second-order autoregressive CAR(2) error process was incorporated into the models to minimize the effect of autocorrelation inherent in the longitudinal data used, and to provide valid tests of significance for model parameter estimates. In general, variable-form taper functions provided the most accurate predictions. The flexibility and predictive performance of the variable-form model developed by Kozak (For Chron 80(4):507–515, 2004) indicated its usefulness for estimating diameter at a specific height, merchantable volume, and total volume of Maritime pine in the study area.     

Stem taper equation analysis for Larix kaempferi species in the Central Region of South Korea

Taper equation was developed to predict diameters at specific height for Larix kaempferi species in the Central Region of South Korea. The sampled trees that were collected through destructive sampling ranged from 0.60 to 47.90 cm DBH with total height ranging from 2.00 to 33.00 m. The dataset was randomly split into two: 80% for initial model fitting and 20% for model validation. The combined that means 100% dataset was used for final model fitting. Statistics of fit were used as criteria, including the coefficient of determination (R²), standard error of the estimate (SEE), bias (ē), the absolute mean difference (AMD), and the Akaike information criterion (AIC) values and weight (AICw), with a rank analysis being applied. Initial model fitting utilized a total of nine taper equations, with the three segmented taper equations and another three non-segmented determined for model validation and final model fitting. Kozak02 equation, which had not yet been evaluated for L. kaempferi species, indicated the best performance for the species in the Central Region of South Korea. Upon comparison, the ability of this study to predict diameters at specific height and stem volume was better than the existing taper equation for L. kaempferi in South Korea.     

Tree taper models for Cupressus lusitanica plantations in Ethiopia

To provide a taper model for planning and management of Cupressus lusitanica plantations in Ethiopia, seven taper models were compared. Four performance indicator statistics were used for comparing the models in their ability to estimate tree diameter, and total and merchantable volumes. For the selected species, Kozak (1988) was found to be the best, followed by modified Lee et al. (2003) and Kozak (2004) as second and third best taper models, respectively. Both the Kozak (Kozak, 1988, 2004) and the modified Lee et al. (2003) models were very flexible in capturing the different shapes of trees. In particular, Kozak (2004) proved to be best of all models in diameter estimation even though it was found to be inferior to the Kozak (1988) and modified Lee et al. (2003) models for total and merchantable volume estimation. To understand the influence of the inflection point p in the Kozak (1988) model, Monte Carlo simulation was used to examine sensitivity of the model performance against inflection point p. In this effort, slightly lower standard errors were observed for p between 0.1 and 0.3. Mixed effects modeling was also used to further study the inflection point p as a random effect. The empirical Bayes estimates of the random effects were found to vary from tree to tree and also appear to depend on tree size. The results from both the Monte Carlo and mixed effects modeling study seem to indicate the need to estimate p from the data.     

Stem taper functions for Betula platyphylla in the Daxing'an Mountains,northeast China

Accurate prediction of stem diameter is an important prerequisite of forest management.In this study,an appropriate stem taper function was developed for upper stem diameter estimation of white birch(Betula platyphylla Sukaczev) in ten sub-regions of the Daxing'an Mountains,northeast China.Three commonly used taper functions were assessed using a diameter and height dataset comprising 1344 trees.A first-order continuous-time error structure accounted for the inherent autocorrelation.The segmented model of Max and Burkhart(For Sci 22:283-289,1976.https://doi.org/10.1093/forestscience/22.3.283) and the variable exponent taper function of Kozak(For Chron 80:507-515,2004.https://doi.org/10.5558/tfc80507-4) described the data accurately.Owing to its lower multicollinearity,the Max and Burkhart(1976) model is recommended for diameter estimation at specific heights along the stem for the ten sub-regions.After comparison,the Max and Burkhart(1976) model was refitted using nonlinear mixed-effects techniques.Mixed-effects models would be used only when additional upper stem diameter measurements are available for calibration.Differences in region-specific taper functions were indicated by the method of the non-linear extra sum of squares.Therefore,the particular taper function should be adjusted accordingly for each sub-region in the Daxing'an Mountains.     

兴安落叶松天然林削度方程的研究

削度方程具有不受材种规格的限制、应用简便等优点,现已成为编制材种出材率表基础工作。本文以大兴安岭东部地区兴安落叶松天然林为研究对象,利用776株林木干形数据,通过分析、比较和评价4个削度方程拟合效果和预估精度,确定了兴安落叶松最佳削度方程。     

The impact of cronartium flaccidum on the growth of pinus sylvestris

The blister rust of two‐needle pines in Europe is caused by the rust fungus, Cronartium flaccidum (Alb. Schw.) Wint. There are two races of the fungus: One host‐alternating and another pine‐to‐pine race. The latter race is considered to be more common in northern Sweden. The impact of this rust on growth of Scots pine (Pinus sylvestris L.) was investigated in three selected stands in northern Sweden. Radial stem increment was reduced 40–70% by severe attacks and 20–40% by minor attacks. The reduction of stem volume growth was probably greater. The faster growing trees seemd to be more severely attacked. Trees growing on poor soils appeared to lose almost as much growth capacity from a minor attack as from a severe attack.     

Modeling top height growth of red alder plantations

Height growth equations for dominant trees are needed for growth and yield projections, to determine appropriate silvicultural regimes, and to estimate site index. Red alder [Alnus rubra Bong.] is a fast-growing hardwood species that is widely planted in the Pacific Northwest, USA. However, red alder dominant height growth equations used currently have been determined using stem analysis trees from natural stands rather than repeated measurements of stand-level top height from plantations, which may cause them to be biased. A regional dataset of red alder plantations was complied and used to construct a dynamic base-age invariant top height growth equation. Ten anamorphic and polymorphic Generalized Algebraic Difference Approach (GADA) forms were fit using the forward difference approach. The Chapman–Richards anamorphic and Schumacher anamorphic model forms were the only ones with statistically significant parameters that yielded biologically reasonable predictions across a full range of the available data. The Schumacher model form performed better on three independent datasets and, therefore, was selected as the final model. The resulting top height growth equations differed appreciably from tree-level dominant height growth equations developed using data from natural stands, particularly at the younger ages and on lower site indices. Both the rate and shape parameters of the Schumacher function were not influenced by initial planting density. However, this analysis indicates that the asymptote, which is related to site index, may be reduced for plantations with initial planting density below 500 trees ha⁻¹. The final equation can be used for predictions of top height (and thus) site index for red alder plantations across a range of different growing conditions.     

Evaluation of growth response,stand value and financial return for pre-commercially thinned jack pine stands in Northwestern Ontario

This study examined the impact of pre-commercial thinning (PCT) on tree growth, product recovery, stand value and financial return in jack pine stands in Northwestern Ontario. Ten sites composed of both control and PCT stands representing various stand densities (2000–6000 trees/ha) and stand ages (26–36 years old) were selected for this study. Three thousand and eighty-two trees were measured for DBH and total height, and were reconstructed in 3-D using a taper equation for jack pine. The reconstructed virtual trees were then “sawn” using the software package Optitek to obtain optimal lumber value recovery, which was then used to determine total product value per tree and financial return. The quadratic mean DBHs of trees from the PCT stands were significantly larger than those from the control stands for all 10 sites. Six of ten PCT stands had significantly taller trees than did the controls of the same sites. With increasing stand density, tree DBH decreased in the control stands while no consistent pattern could be recognized for the DBH of the PCT stands. The increment in average DBH due to PCT increased with increasing thinning intensity. PCT reduced total tree volume per hectare, benefited merchantable stem volume per hectare, and improved the total lumber volume and value recovery per hectare. On average, the PCT stands produced approximately $2760 and $1770/ha (or 19.6 and 16.1%) more product value per hectare for the dimension mill and stud mill, respectively. PCT also significantly reduced logging and lumber conversion costs. Higher total product values and lower total costs resulted in higher benefit/cost (B/C) ratios in the PCT stands than did in the control stands. The increased financial return due to PCT is associated with the magnitude of difference in quadratic mean DBH resulting from PCT. The B/C ratio difference between control and PCT stands increased with increasing thinning intensity. Overall, this study indicates that PCT appears to be an economically viable silvicultural investment for jack pine stands in Northwestern Ontario.     

Derivation of stem taper from the pipe theory in a carbon balance framework

A dynamic tree growth model is described. The model derives the development of stem taper and vertical distribution of branch basal area from the pipe model, assuming that reuse of active pipes is regulated by foliage dynamics in a vertically explicit crown with a foliage distribution of constant shape. Based on empirical findings, the pipe model was modified slightly to allow the foliage/sapwood ratio to vary as a function of distance from the treetop. Growth was derived from carbon balance in a stand of different size trees that may shade each other. The model was applied to old and middle-aged trees growing in dense and sparse stands of Scots pine for which stand-level measurements are available as a chronosequence, but individual trees have been measured only once. Measured trees were compared with corresponding simulated trees for stem taper and vertical distribution of branch basal area. The results indicated that the pipe model assumptions, combined with a model of tree growth, are capable of producing realistic predictions of the vertical distribution of stem and branch diameter in trees of different sizes in the stand. A comparison of the results with a simple form of the uniform stress theory showed good agreement between the two models. However, a significant difference was found between the measured relative contribution of heartwood to total stem diameter and the predicted share of disused pipes in the stem. A possible explanation for this discrepancy is that the transition from sapwood to heartwood is gradual rather than abrupt as assumed in the model. A modification of the pipe model to incorporate a gradual transition is outlined.     

Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta,Canada

Four variable-exponent taper equations and their modified forms were evaluated for lodgepole pine (Pinus contorta var. latifolia Engelm.) trees in Alberta, Canada. A nonlinear mixed-effects modeling approach was applied to account for within- and between-tree variations in stem form. Even though a direct modeling of within-tree autocorrelation by a variance–covariance structure failed to achieve convergence, most of the autocorrelation was accounted for when random-effects parameters were included in the models. Using an independent data set, the best taper equation with two random-effects parameters was chosen based on its ability to predict diameter inside bark, whole tree volume, and sectioned log volume. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 5.3 m above ground was best suited for calibrating tree-specific predictions of diameter inside bark, whole tree volume, and sectioned log volume.     

Site index models for Calabrian pine in the central Mediterranean region of Turkey

Stem analysis data of 432 trees were obtained from even-aged, pure natural stands of Calabrian pine in the central Mediterranean Region of Turkey. Eight dynamic site equations derived with the Generalized Algebraic Difference Approach (GADA) were compared, based on autoregressive analysis and a thorough evaluation of the goodness of fit. We used generalized nonlinear least squares methods for model fitting. The adjusted coefficients of determination (0.9825–0.9842), root-mean-square errors (0.8004–0.8435 m), and Akaike’s information criterion differences (0–145) indicated a good fit of the eight site index equations. The Hossfeld equation (M3) provided the best result. The Durbin-Watson test statistic did not reveal an autocorrelation issue while the Hossfeld equation provided a satisfactory solution to the serial correlation problem in stem analysis data as time series using autoregressive modeling. This study presents new site index models for Calabrian pine forests in the central Mediterranean region of Turkey where it is the most important commercial tree species. The site index equation, based on the Hossfeld model is recommended for height growth prediction and site classification of Calabrian pine stands in the central Mediterranean region of Turkey, providing a new basis for growth prediction and yield estimation in these important forest ecosystems.